Hip roofs and hip rafters are well known in the architecture and building construction arts.
A hip roof is commonly defined in the art as a roof having sloping sides and sloping ends, and a hip rafter is a rafter extending from the wall plate to the ridge and forming the angle of the hip roof. Although the definition of hip roof includes both the sides and the end, for purposes of discussion herein, the following definitions are used for the parts of a hip roof: a) the portion of the roof having a ridge beam and common rafters attaching to the sides of the ridge beam is referred to as the main roof; and b) the portion of the roof having hip rafters attaching to the end of the ridge beam and jack rafters attaching to the hip rafters is referred to as the hip roof.
A roof valley is commonly defined in the art and used herein as a place of meeting of two slopes of a roof that form a re-entrant angle, and a valley rafter is a rafter running from the wall plate along the valley to the ridge.
A roof slope or pitch is commonly defined in the art and used herein as the rise of the roof from wall plate to ridge divided by the horizontal run of the roof on the plan. Roof pitch in the United States is typically expressed as a ratio having the denominator 12, although other pitches and other measurement systems such as metric are fully comprehended by the present invention.
Plan angle refers to an angle between two non-horizontal elements when projected onto a horizontal surface such as the surface defined by the wall plates of the building.
Common rafters are rafters in a main roof extending orthogonally from the side wall plate to the ridge. A hip rafter meets the ridge at the joining point of the last common rafter to the ridge. Jack rafters are shorter rafters extending from the side wall plate or end wall plate to a hip rafter, or from the ridge to a valley rafter.
For clarity, the following presentation deals only with hip rafters, but those of ordinary skill in the carpenterial arts will recognize that the presentation and present invention are equally applicable to valley rafters.
In building a conventionally-framed wood building having a hip roof, the lengths and cutting angles for the hip rafters from raw planks, and the correct nailing locations for jack rafters to the hip rafters, must be determined.
A typical hip roof has two identical hip rafters symmetrically arranged on either side of, and meeting at, the end of the roof ridge (which typically although not necessarily contains a horizontal ridge pole or ridge beam). Generally, a hip rafter bisects the meeting angle of the side wall and end wall plates. Thus, in a typical hip roof for rectangular construction the side wall and end wall plates meet at a 90° angle and the hip rafter bisects the angle, meeting both plates at a 45° angle to each one. In other constructions, for example octagonal, the side wall and end wall plates meet at an included 135° angle, and the hip rafter bisects that angle and meets both plates at a 67.5° angle.
When the hip rafter bisects the plate angle, the pitch of the main roof and the hip roof must be the same. However, in other roofs wherein the hip rafter does not bisect the plate angle, the hip roof pitch must differ from the main roof pitch. Such cases show that of the two angles formed by the hip rafter, only the angle formed with the last common rafter is important in laying out the hip rafter.
Thus, the laying out of a hip rafter requires simultaneous combining of the main roof pitch, the actual roof rise, and the plan or projected meeting angle between the hip rafter and the end wall plate. In the prior art, the layout of the hip rafter is accomplished in a wide variety of ways, from calculation by the Pythagorean Theorem to use of direct measurement and tables of trigonometric functions. All of these are difficult, time-consuming, and require in the carpenter a good understanding of three-dimensional trigonometry.
What is needed in the art is a simple framing tool that can incorporate the required trigonometric functions directly to allow easy measurement and marking of cuts and rafter nailing patterns in laying out a hip rafter.
It is a principal object of the present invention to simplify and make more reliable the creation of a hip rafter for a hip roof.